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Fractional dynamics of an infection model with time-varying drug exposure

[+] Author and Article Information
Carla Pinto

School of Engineering, Polytechnic of Porto, Rua Dr Antnio Bernardino de Almeida, 431, Porto 4249-015, Portugal
cap@isep.ipp.pt

Ana Carvalho

Faculty of Sciences, University of Porto, Rua do Campo Alegre s/n, 4440-452 Porto, Portugal
up200802541@fc.up.pt

1Corresponding author.

ASME doi:10.1115/1.4038643 History: Received June 14, 2017; Revised November 15, 2017

Abstract

We introduce a fractional order model for HIV dynamics where time-varying drug-exposure and drug-resistance are assumed. We derive conditions for the local and global asymptotic stability of the disease-free equilibrium. We find periodic stable endemic states for certain parameter values, for sinusoidal drug efficacies and when considering a density dependent decay rate for the $T$ cells. Other classes of periodic drug-efficacies are considered and the effect of the phases of these functions on the dynamics of the model are also studied. The order of the fractional derivative plays an important role in the severity of the epidemics.

Copyright (c) 2017 by ASME
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